Analytic calculation method, system and equipment for transient voltage and current of power grid fault

Abstract

The invention discloses an analytical calculation method, system and equipment for transient voltage and current of a power grid fault. The method comprises the following steps: constructing a fault resistance network matrix; calculating a voltage and current initial traveling wave at the fault point by adopting phase-mode transformation at least based on the fault resistance network matrix; constructing a fault component additional network; respectively calculating a first traveling wave refraction and reflection coefficient at a fault point and a second traveling wave refraction and reflection coefficient at a non-fault point in the fault component additional network; respectively acquiring all first traveling wave propagation paths and all second traveling wave propagation paths, and calculating the total propagation time and the total traveling wave refraction and reflection coefficient on each traveling wave propagation path at least based on the first traveling wave refraction and reflection coefficient and the second traveling wave refraction and reflection coefficient; and at least based on the total propagation time and the total traveling wave refraction and reflection coefficient, performing summation and superposition to obtain a fault transient voltage and current analytic expression. According to the method, a reliable theoretical basis can be provided for development of a relay protection and fault positioning technology based on high-frequency transient information.

Description

Technical Field

[0001] The present invention relates to the technical field of power system fault analysis, and in particular to a method, system and device for analyzing and calculating transient voltage and current of power grid faults. Background Art

[0002] In recent years, the development of power systems has been very rapid, the grid structure has become increasingly complex, and the requirements for safe and stable operation of the system have been continuously improved. Traditional relay protection and fault location technology based on power frequency fault information requires filtering of power frequency electrical quantities, and the data window added during processing must be long enough, which is inconsistent with the requirements for the speed of relay protection. Moreover, the transient traveling wave after the fault contains a large amount of fault characteristic information, such as fault phase, fault location, and fault time. In the field of power system relay protection today, relay protection and fault location technology based on high-frequency transient information has become a widely concerned research direction. Therefore, it is necessary to analyze and calculate the transient voltage and current after the power grid fault, so as to provide a theoretical basis for the development of the above technology.

[0003] At present, the analysis and calculation of power grid fault voltage and current can be divided into two categories according to the solution method: analytical method and numerical method. The analytical method establishes the equation of the fault network and expresses the solution of the equation as a function of known parameters, thereby calculating the accurate analytical results. The numerical method usually uses difference instead of differential, and equates the power grid to the form of impedance and historical current source in parallel, and calculates the fault voltage and current point by point according to the step size. It is easy to program and can be widely used in electromagnetic transient simulation software. However, the numerical method can only obtain the point-by-point waveform of the fault voltage and current, and the mathematical and physical meaning is not clear, and it is difficult to understand the intrinsic relationship between the fault voltage and current and the various parameters; while the analytical method is only applicable to a very small number of simple cases, avoiding the diversity and complexity of the actual power grid. Summary of the invention

[0004] The purpose of the present invention is to propose a new method for analyzing and calculating the voltage and current of power grid faults, which can adapt to various complex scenarios, obtain fault analysis results, and support the research on relay protection and fault location technology based on high-frequency transient information. In order to achieve the above purpose, the present invention provides a method, system and device for analyzing and calculating the transient voltage and current of power grid faults.

[0005] In a first aspect, an embodiment of the present invention provides a method for analyzing and calculating transient voltage and current of a power grid fault, comprising:

[0006] At least based on the fault type of the target power system, construct a corresponding fault resistor network matrix;

[0007] At least based on the fault resistance network matrix, using phase mode transformation to calculate the initial traveling waves of voltage and current at the fault point;

[0008] Based on the initial traveling waves and cross transmissions of the voltage and current at the fault point, construct a fault component additional network; wherein the fault component additional network is in the form of a weighted directed graph and includes a zero mode network and a line mode network, the zero mode network includes a zero mode measurement point, and the line mode network includes a line mode measurement point;

[0009] Based on the fault point characteristics, respectively calculating the first row wave refraction reflection coefficient at the fault point and the second row wave refraction reflection coefficient at the non-fault point in the fault component additional network; wherein the fault point characteristics include connecting the zero mode network and the line mode network;

[0010] Respectively obtain all first traveling wave propagation paths from the fault point to the zero-mode measurement point and all second traveling wave propagation paths from the fault point to the line-mode measurement point, and calculate the total propagation time and the total traveling wave refraction reflection coefficient on each traveling wave propagation path based at least on the first traveling wave refraction reflection coefficient and the second traveling wave refraction reflection coefficient;

[0011] At least based on the total propagation time and the total traveling wave refraction reflection coefficient, the fault transient voltage and current analytical formula is obtained by summing and superposition.

[0012] Preferably, the step of constructing a corresponding fault resistance network matrix based at least on the fault type of the target power system includes:

[0013] Determine a resistance network and a fault type of a target power system; wherein the resistance network includes at least a resistance connection mode;

[0014] Establishing an initial equation between node voltage and node current based on electrical characteristics of the resistor network; wherein the electrical characteristics of the resistor network at least include Ohm's law;

[0015] Introducing corresponding fault components into the initial equation based on the fault type to obtain a target equation; wherein the fault components include resistance changes of each resistor;

[0016] The target equation is converted into a matrix form to obtain a fault resistance network matrix.

[0017] Preferably, the calculating of the initial traveling waves of voltage and current at the fault point by using phase mode transformation at least based on the fault resistance network matrix comprises:

[0018] Based on the corresponding relationship between the initial traveling wave phasors of voltage and current, the initial traveling wave phasor of voltage at the fault point and the initial traveling wave phasor of current flowing to one end of the bus are determined; wherein the corresponding relationship between the initial traveling wave phasors of voltage and current is characterized by the following formula:

[0019] u ph +u f +2Ri ph =0

[0020] Among them, u ph represents the initial traveling wave phase of the voltage at the fault point, u f represents the voltage at the fault point before the fault occurs, R represents the fault resistance network matrix, i ph It represents the initial traveling wave phasor of the current flowing to one end of the bus;

[0021] The voltage initial traveling wave modulus and the current initial traveling wave modulus are determined based on the corresponding relationship between the voltage and current initial traveling wave modulus; wherein the corresponding relationship between the voltage and current initial traveling wave modulus is characterized by the following formula:

[0022] u m =Zi m

[0023] Among them, u m represents the initial traveling wave modulus of voltage, i m represents the initial traveling wave modulus of the current, and Z represents the wave impedance matrix;

[0024] Phase-to-mode transformation is performed based on the voltage initial traveling wave phasor, the current initial traveling wave phasor, the voltage initial traveling wave modulus and the current initial traveling wave modulus to obtain the voltage and current initial traveling waves at the fault point.

[0025] Preferably, performing phase-mode transformation based on the voltage initial traveling wave phasor, the current initial traveling wave phasor, the voltage initial traveling wave modulus and the current initial traveling wave modulus to obtain the voltage and current initial traveling waves at the fault point includes:

[0026] The initial voltage traveling wave phasor, the initial current traveling wave phasor, the initial voltage traveling wave modulus and the initial current traveling wave modulus are transformed into phase mode by using the Karenbauer transformation matrix to obtain the initial voltage and current traveling waves at the fault point; wherein the initial voltage and current traveling waves at the fault point are expressed by the following formula:

[0027]

[0028] Among them, u m represents the initial traveling wave modulus of voltage, i m represents the initial traveling wave modulus of the current, Z represents the wave impedance matrix, S represents the Karenbauer transformation matrix, R represents the fault resistance network matrix, u f Indicates the voltage at the fault point before the fault occurs.

[0029] Preferably, the construction of the fault component additional network based on the initial traveling wave and cross transmission of the voltage and current at the fault point includes:

[0030] Based on the initial traveling waves of voltage and current at the fault point, a zero-mode network and a line-mode network are respectively constructed;

[0031] Based on the cross transmission at the fault point, the zero mode network and the fault point in the line mode network are connected to obtain an initial fault component additional network;

[0032] The initial fault component additional network is characterized in the form of a weighted directed graph to obtain a fault component additional network; wherein the vertices of the weighted directed graph represent the nodes of the fault component additional network, the branches of the weighted directed graph represent the lines of the fault component additional network, the directions of the branches represent the propagation directions of the traveling waves on the lines, and the weights of the branches represent the propagation time of the traveling waves on the lines.

[0033] Preferably, the calculating of the first wave refraction reflection coefficient at the fault point and the second wave refraction reflection coefficient at the non-fault point in the fault component additional network based on the fault point characteristics respectively includes:

[0034] Based on the fault point characteristics, the first line wave refraction reflection coefficient at the fault point in the fault component additional network is calculated; wherein the first line wave refraction reflection coefficient is calculated using the following formula:

[0035]

[0036] Among them, α represents the first wave refraction coefficient, β represents the first wave reflection coefficient, I represents the unit matrix, Z represents the wave impedance matrix, S represents the Karenbauer transformation matrix, and R represents the fault resistance network matrix;

[0037] A complex frequency domain model is used to characterize the non-fault point, and the second-line wave refraction reflection coefficient at the non-fault point is calculated based on the obtained non-fault point model; wherein the non-fault point model includes a lumped parameter element connected in series between the lines and a lumped parameter element connected in parallel between the lines and the earth.

[0038] Preferably, the steps of respectively acquiring all first traveling wave propagation paths from the fault point to the zero mode measurement point and all second traveling wave propagation paths from the fault point to the line mode measurement point, and calculating the total propagation time and the total traveling wave refraction reflection coefficient on each traveling wave propagation path based at least on the first traveling wave refraction reflection coefficient and the second traveling wave refraction reflection coefficient, include:

[0039] Using a recursive algorithm to respectively obtain all first traveling wave propagation paths from the fault point to the zero-mode measurement point and all second traveling wave propagation paths from the fault point to the line-mode measurement point;

[0040] The propagation time of all lines on each traveling wave propagation path is added up to obtain the total propagation time on the corresponding traveling wave propagation path;

[0041] The traveling wave refraction and reflection coefficients of all nodes passed by each traveling wave propagation path are multiplied together to obtain the total traveling wave refraction and reflection coefficient on the corresponding traveling wave propagation path.

[0042] Preferably, the analytical formula of the fault transient voltage and current is obtained by summing and superposing at least based on the total propagation time and the total traveling wave refraction reflection coefficient, including:

[0043] Based on the summation operation of the total propagation time and the total traveling wave refraction and reflection coefficient, the complex frequency domain analytical expression of the traveling wave at the measurement point is obtained; wherein the complex frequency domain analytical expression of the voltage traveling wave is represented by the following formula:

[0044]

[0045] Among them, U mf (s) represents the voltage traveling wave complex frequency domain, γ i (s) represents the total wave refraction reflection coefficient, U i (s) represents the complex frequency domain form of the initial voltage traveling wave, s represents the complex frequency, t i represents the total propagation time;

[0046] Performing an inverse Laplace transform on the complex frequency domain analytical expression of the traveling wave, and performing a phase mode transform on the obtained time domain solution to obtain a traveling wave time domain phasor;

[0047] The traveling wave time domain phasors are superimposed to obtain the fault transient voltage and current analytical formula; wherein the fault transient voltage analytical formula is represented by the following formula:

[0048] u m (t) = u 0 (t)+u mf (t)

[0049] Among them, u m (t) represents the fault transient voltage, u 0 (t) represents the voltage at the measuring point before the fault, u mf (t) represents the voltage traveling wave time domain phasor.

[0050] In a second aspect, an embodiment of the present invention provides a system for analyzing and calculating transient voltage and current of a power grid fault, comprising:

[0051] A fault resistor network matrix building module is used to build a corresponding fault resistor network matrix based on at least the fault type of the target power system;

[0052] A voltage and current initial traveling wave calculation module, used to calculate the voltage and current initial traveling waves at the fault point by using phase mode transformation based at least on the fault resistance network matrix;

[0053] A fault component additional network construction module is used to construct a fault component additional network based on the voltage and current initial traveling waves and cross transmission at the fault point; wherein the fault component additional network is in the form of a weighted directed graph and includes a zero mode network and a line mode network, the zero mode network includes a zero mode measurement point, and the line mode network includes a line mode measurement point;

[0054] A traveling wave refraction reflection coefficient calculation module is used to calculate the first traveling wave refraction reflection coefficient at the fault point and the second traveling wave refraction reflection coefficient at the non-fault point in the fault component additional network based on the fault point characteristics; wherein the fault point characteristics include connecting the zero mode network and the line mode network;

[0055] A traveling wave propagation path calculation module, used to respectively obtain all first traveling wave propagation paths from the fault point to the zero-mode measurement point and all second traveling wave propagation paths from the fault point to the line-mode measurement point, and calculate the total propagation time and the total traveling wave refraction reflection coefficient on each traveling wave propagation path based at least on the first traveling wave refraction reflection coefficient and the second traveling wave refraction reflection coefficient;

[0056] The fault transient voltage and current analysis module is used to obtain the fault transient voltage and current analysis formula by summing and superposition based at least on the total propagation time and the total traveling wave refraction reflection coefficient.

[0057] In a third aspect, an embodiment of the present invention provides a terminal device, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor implements the analytical calculation method for transient voltage and current of power grid faults as described above when executing the computer program.

[0058] Compared with the prior art, the analytical calculation method, system and device of transient voltage and current of power grid fault in the embodiment of the present invention have the beneficial effect of being able to obtain analytical expressions of transient voltage and current of power grid fault, with clear mathematical and physical meanings, and being adaptable to various fault types, different fault transition resistances, different power grid topologies, and different line parameters. For uniformly transposed lossless lines, without considering the parameter-dependent characteristics, the analytical expression obtained is completely accurate, thereby providing a reliable theoretical basis for the development of relay protection and fault location technology based on high-frequency transient information. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a schematic diagram of network decomposition after a failure in an embodiment of the present invention;

[0060] Figure 2 is a schematic diagram of traveling wave propagation according to an embodiment of the present invention;

[0061] Figure 3It is a flow chart of a method for analyzing and calculating transient voltage and current of a power grid fault according to an embodiment of the present invention;

[0062] Figure 4 It is a schematic diagram of a process of constructing a fault resistance network matrix according to an embodiment of the present invention;

[0063] Figure 5 is a schematic diagram of the structure of a fault resistance network according to an embodiment of the present invention;

[0064] Figure 6 It is a schematic diagram of a flow chart of calculating the initial traveling waves of voltage and current at a fault point according to an embodiment of the present invention;

[0065] Figure 7 It is a schematic diagram of a process of constructing a fault component additional network according to an embodiment of the present invention;

[0066] Figure 8 is a schematic diagram of the structure of a fault component additional network according to an embodiment of the present invention;

[0067] Fig. 9 1 is a schematic diagram of a flow chart of calculating a traveling wave refraction reflection coefficient according to an embodiment of the present invention;

[0068] Fig.10 is a schematic diagram of a non-fault point model according to an embodiment of the present invention;

[0069] Fig.11 It is a schematic diagram of a flow chart of calculating the total propagation time and the total traveling wave refraction reflection coefficient according to an embodiment of the present invention;

[0070] Fig.12 It is a flow chart of obtaining the fault transient voltage and current analytical formula according to an embodiment of the present invention;

[0071] Fig.13 It is a structural schematic diagram of an analytical calculation system for transient voltage and current of a power grid fault;

[0072] Fig.14 is a schematic diagram of the structure of a terminal device according to an embodiment of the present invention;

[0073] Figure 1 In the equation, U1~U2 are voltage sources; uf is the voltage at the fault point before the fault; -uf is the voltage at the fault point after the fault; Rf is the fault transition resistance;

[0074] Figure 2 In, f, fault point; t 1 ,t 2 ,t 3 , impedance discontinuity point;

[0075] Figure 5 In the middle, Ra~Rg, resistance;

[0076] Figure 8Middle,U 1 ~U 2 , voltage source; 0, fault point; 1~8, lumped parameter element; Z 1 ~Z 2 , wave impedance; L 1 ~L 13 , line; Rf, fault transition resistance; Uf, voltage source at the fault point. DETAILED DESCRIPTION

[0077] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0078] In the description of the present invention, it should be understood that the terms "first" and "second" etc. are used in the present invention to distinguish different objects rather than to describe a specific order.

[0079] When a power grid suddenly fails, the entire power system can be regarded as a linear system in a short period of time, which satisfies the superposition principle. At this time, the network after the failure can be equivalent to the superposition of the network before the failure and the network with fault components after the failure. Figure 1 As shown in the figure, in the fault component additional network at this time, there is a voltage source at the fault point, and its voltage is opposite to the voltage at the point before the fault (voltage amplitude is equal and polarity is opposite). Under the action of this voltage source, the traveling wave will start from the fault point and propagate along the line to the busbars on both sides.

[0080] When a fault occurs in the power system, the initial traveling wave will be emitted from the fault point and propagate throughout the power network. Every time the fault traveling wave passes through a measuring point, a new traveling wave signal will be superimposed on the original electrical quantity measured at the measuring point. Figure 2 As shown in the figure, when a fault occurs in the power system at point f, the traveling wave propagates along the line to both ends. When the traveling wave propagates to the point of wave impedance discontinuity, refraction and reflection will occur.

[0081] like Figure 3 As shown, an embodiment of the present invention provides a method for analyzing and calculating transient voltage and current of a power grid fault, comprising the steps of:

[0082] S1. constructing a corresponding fault resistance network matrix based on at least the fault type of the target power system;

[0083] Specifically, Figure 4 As shown, step S1 includes:

[0084] S101, determining a resistance network and a fault type of a target power system;

[0085] The resistor network at least includes a resistor connection mode, and the fault type at least includes a line short circuit.

[0086] S102, establishing an initial equation between node voltage and node current based on electrical characteristics of the resistor network;

[0087] The electrical characteristics of resistor networks include at least Ohm's law.

[0088] S103, introducing corresponding fault components into the initial equation based on the fault type to obtain a target equation;

[0089] The fault component consists of the resistance change of each resistor.

[0090] S104, converting the target equation into a matrix form to obtain a fault resistance network matrix.

[0091] Specifically, the coefficients and unknowns in the target equation are organized into a matrix form to form a fault resistance network matrix.

[0092] The target power system of this embodiment is a three-phase system. Figure 5 As shown in Figure 1, it is a fault resistance network for a three-phase system. Figure 5 The resistance values ​​of the four resistors (Ra, Rb, Rc, Rg) can represent different line fault types. For example, for a single-phase grounding fault of phase A, Rb and Rc can be set to infinity, Ra can be set to the fault transition resistance, and Rg can be set to 0. Furthermore, other types of faults can be realized by changing the resistance values ​​of the four resistors. At this time, the fault resistance network matrix R is as follows:

[0093]

[0094] S2, at least based on the fault resistance network matrix, using phase mode transformation to calculate the initial traveling waves of voltage and current at the fault point;

[0095] Specifically, Figure 6 As shown, step S2 includes:

[0096] S201, determining the initial voltage traveling wave phasor at the fault point and the initial current traveling wave phasor flowing to the bus at one end based on the corresponding relationship between the initial voltage and current traveling wave phasors;

[0097] Specifically, the following formula is used to characterize the initial traveling wave phasor correspondence between voltage and current:

[0098] u ph +u f +2Ri ph =0

[0099] Among them, u ph represents the initial traveling wave phase of the voltage at the fault point, u frepresents the voltage at the fault point before the fault occurs, R represents the fault resistance network matrix, i ph Represents the initial traveling wave phasor of the current flowing to one end of the bus.

[0100] For this embodiment, u f =[u af u bf u cf ] T It indicates the three-phase voltage at the fault point before the fault occurs. If the fault occurs at t 0 At this moment, u xf =A x sin(ωt+θ x )ε(tt 0 ), x∈[a,b,c], ε represents the unit step function, A x represents the voltage amplitude at the fault point before the fault, (ωt+θ x ) represents the voltage phase angle at the time of fault occurrence.

[0101] S202, determining an initial traveling wave modulus of voltage and an initial traveling wave modulus of current based on a corresponding relationship between initial traveling wave moduli of voltage and current;

[0102] Specifically, the following formula is used to characterize the correspondence between the voltage and current initial traveling wave modulus:

[0103] u m =Zi m

[0104] Among them, u m represents the initial traveling wave modulus of voltage, i m represents the initial traveling wave modulus of the current, and Z represents the wave impedance matrix.

[0105] For this embodiment, Z = diag (Z 0 ,Z 1 ,Z 1 ) represents the wave impedance matrix, Z 0 and Z 1 They represent zero-mode wave impedance and line-mode wave impedance respectively.

[0106] S203 , performing phase-to-mode transformation based on the voltage initial traveling wave phasor, the current initial traveling wave phasor, the voltage initial traveling wave modulus, and the current initial traveling wave modulus to obtain the voltage and current initial traveling waves at the fault point.

[0107] Specifically, the Karenbauer transformation matrix is ​​used to perform phase-mode transformation on the voltage initial traveling wave phasor, the current initial traveling wave phasor, the voltage initial traveling wave modulus and the current initial traveling wave modulus to obtain the voltage and current initial traveling waves at the fault point.

[0108] The following formula is used to express the initial traveling wave of voltage and current at the fault point:

[0109]

[0110] Among them, u m represents the initial traveling wave modulus of voltage, i m represents the initial traveling wave modulus of the current, Z represents the wave impedance matrix, S represents the Karenbauer transformation matrix, R represents the fault resistance network matrix, u f Indicates the voltage at the fault point before the fault occurs.

[0111] In this embodiment, for a uniformly transposed lossless line, without considering frequency-varying parameters, a Karenbauer transformation matrix is ​​used to perform phase-to-mode transformation on the phasor and modulus of voltage and current to achieve decoupling between the three phases.

[0112] u ph =Su m ,i ph =Si m

[0113]

[0114] The initial traveling waves of voltage and current in the mode domain can be solved:

[0115]

[0116] By adjusting the S, Z and R matrices, the above formula can be applied to calculate the initial traveling waves of voltage and current at the fault point on any multi-phase parallel multi-conductor line.

[0117] S3, constructing the fault component additional network based on the initial traveling wave and cross transmission of voltage and current at the fault point;

[0118] The fault component additional network is in the form of a weighted directed graph and includes a zero-mode network and a line-mode network. The zero-mode network includes a zero-mode measurement point, and the line-mode network includes a line-mode measurement point.

[0119] Specifically, Figure 7 As shown, step S3 includes:

[0120] S301, constructing a zero-mode network and a line-mode network based on the initial traveling waves of voltage and current at the fault point;

[0121] When constructing the fault component additional network, the voltage source in the original network is short-circuited and the current source is open-circuited, and a voltage source that generates the initial traveling wave is set at the fault point. For uniformly transposed parallel multi-conductor lines, they can be regarded as zero-mode networks and line-mode networks, and their topological structures are exactly the same, but the wave speed and wave impedance are different.

[0122] S302, based on the cross transmission at the fault point, connecting the fault points in the zero mode network and the line mode network to obtain an initial fault component additional network;

[0123] Since the modulus traveling wave at the fault point may have cross-transmission phenomenon, the fault points in the zero-mode network and the line-mode network should be connected and regarded as one node, so as to obtain the power network after the fault, that is, the initial fault component additional network.

[0124] S303 , characterizing the initial fault component additional network in the form of a weighted directed graph to obtain a fault component additional network.

[0125] The vertices of the weighted directed graph represent nodes of the fault component additional network, the branches of the weighted directed graph represent lines of the fault component additional network, the direction of the branch represents the propagation direction of the traveling wave on the line, and the weight of the branch represents the propagation time of the traveling wave on the line.

[0126] like Figure 8 As shown in Figure 1, it is a schematic diagram of the fault component additional network. Each line is a branch in the figure and is given a direction, represented by L. +1 , L -1 , L +2 , L -2 , L +3 , L -3 , ..., "+" in the subscript indicates the positive direction of the branch, and "-" indicates the reverse direction of the branch. Each line is connected by a lumped parameter element, and all lumped parameter elements at the connection (whether connected in series between the lines or in parallel between the line and the earth) are regarded as nodes in the figure, represented as 1, 2, 3, .... The propagation time of the traveling wave on each branch in the figure is used as the weight of the branch. Among them, the propagation time can be obtained by dividing the line length by the wave velocity on the line.

[0127] S4, based on the fault point characteristics, respectively calculate the first line wave refraction reflection coefficient at the fault point in the fault component additional network and the second line wave refraction reflection coefficient at the non-fault point;

[0128] Specifically, Fig. 9 As shown, step S4 includes:

[0129] S401, based on the fault point characteristics, calculating the first line wave refraction reflection coefficient at the fault point in the fault component additional network;

[0130] As a special node, the fault point plays the role of connecting the zero-mode network and the line-mode network, that is, the fault point characteristics include connecting the zero-mode network and the line-mode network. At this time, the refraction-reflection coefficient of the mode domain voltage and current, that is, the refraction-reflection coefficient of the first row wave, is calculated using the following formula:

[0131]

[0132] u ra m =αu i m ,u re m =βu i m ,i ra m =αi i m ,i re m =βi i m

[0133] Where α represents the first wave refraction coefficient, β represents the first wave reflection coefficient, I represents the unit matrix, Z represents the wave impedance matrix, S represents the Karenbauer transformation matrix, R represents the fault resistance network matrix, and u i m ,u re m ,u ra m They represent the voltage incident wave, reflected wave, and refracted wave in the mode domain at the fault point, respectively. i m ,i re m ,i ra m They represent the incident wave, reflected wave and refracted wave of the current in the mode domain at the fault point respectively.

[0134] S402: Use a complex frequency domain model to characterize the non-fault point, and calculate the second-row wave refraction reflection coefficient at the non-fault point based on the obtained non-fault point model.

[0135] For non-fault points, they are characterized as follows Fig.10 The complex frequency domain model shown is the non-fault point model. The non-fault point model includes lumped parameter elements connected in series between the lines and lumped parameter elements connected in parallel between the lines and the earth. 1 , Z 2 , Z 3 , ...Zn represent the wave impedance of each line, Za(s), Zb(s), Zc(s), ...Zx(s) represent the lumped parameter elements (resistance, inductance and capacitance) connected in series between the lines, Z 0 (s) represents a lumped parameter element connected in parallel between the line and the ground.

[0136] Reference Fig.10 , when the traveling wave has a wave impedance of Z 1 The line propagates to the wave impedance Z 2 When the line from Z1 Line to Z 2 The refractive index α(s) of the line and the 1 Line to Z 1 The reflection coefficient β(s) of the line is calculated using the following formula:

[0137]

[0138] in,

[0139] Z 0 ′(s)=Z 0 (s) / / (Z 3 +Z c (s)) / / … / / (Z n +Z x (s))

[0140] S5, respectively obtain all first traveling wave propagation paths from the fault point to the zero mode measurement point and all second traveling wave propagation paths from the fault point to the line mode measurement point, and calculate the total propagation time and the total traveling wave refraction reflection coefficient on each traveling wave propagation path based on at least the first traveling wave refraction reflection coefficient and the second traveling wave refraction reflection coefficient;

[0141] Specifically, Fig.11 As shown, step S5 includes:

[0142] S501, using a recursive algorithm to respectively obtain all first traveling wave propagation paths from the fault point to the zero-mode measurement point and all second traveling wave propagation paths from the fault point to the line-mode measurement point;

[0143] This embodiment uses a computer to find out all the traveling wave propagation paths (first traveling wave propagation path, second traveling wave propagation path) from the fault point to the measurement point within a preset time after the power system fails through a recursive algorithm. Figure 8 , if the fault voltage and current at node 2 are calculated, the entire traveling wave propagation path from fault point 0 to zero-mode measurement point 2 and line-mode measurement point 6 needs to be considered. +11 ―L -11 ―L +12 ―L -12 ―L -8 It can represent one of the traveling wave propagation paths from node 0 to node 6.

[0144] S502, summing up the propagation time of all lines on each traveling wave propagation path to obtain the total propagation time on the corresponding traveling wave propagation path;

[0145] The total propagation time on the traveling wave propagation path can be obtained by summing the weights of each branch on the traveling wave propagation path.

[0146] S503, multiplying the traveling wave refraction and reflection coefficients of all nodes passed by each traveling wave propagation path to obtain the total traveling wave refraction and reflection coefficient on the corresponding traveling wave propagation path.

[0147] S6. Based on at least the total propagation time and the total wave refraction reflection coefficient, the analytical formula of the fault transient voltage and current is obtained by summing and superposition.

[0148] Specifically, Fig.12 As shown, step S6 includes:

[0149] S601, based on the summation operation of the total propagation time and the total traveling wave refraction and reflection coefficient, obtain the complex frequency domain analytical expression of the traveling wave at the measurement point;

[0150] When a fault occurs in the power system, if the complex frequency domain form of the initial voltage traveling wave corresponding to the i-th traveling wave propagation path is U i (s), the complex frequency domain analytical expression of the voltage traveling wave measured at the measuring point in the fault component additional network is as follows:

[0151]

[0152] Among them, U mf (s) represents the voltage traveling wave complex frequency domain, γ i (s) represents the total wave refraction reflection coefficient, U i (s) represents the complex frequency domain form of the initial voltage traveling wave, s represents the complex frequency, t i Represents the total propagation time.

[0153] S602, performing an inverse Laplace transform on the complex frequency domain analytical expression of the traveling wave, and performing a phase mode transform on the obtained time domain solution to obtain a traveling wave time domain phasor;

[0154] S603, performing superposition operation on the traveling wave time domain phasors to obtain an analytical expression of the fault transient voltage and current.

[0155] According to the superposition principle, when a line in the power system fails, the actual voltage at the measuring point, i.e., the fault transient voltage, is expressed as follows:

[0156] u m (t) = u 0 (t)+u mf (t)

[0157] Among them, u m (t) represents the fault transient voltage, u 0 (t) represents the voltage at the measuring point before the fault, which is convenient to obtain, u mf (t) represents the voltage traveling wave time domain phasor.

[0158] The embodiment of the present invention provides an analytical calculation method for transient voltage and current of a power grid fault, which can obtain an analytical expression for transient voltage and current of a power grid fault, has clear mathematical and physical meanings, and is suitable for various fault types, different fault transition resistances, different power grid topologies, and different line parameters. For uniformly transposed lossless lines, without considering parameter-dependent characteristics, the analytical expression obtained is completely accurate, thereby providing a reliable theoretical basis for the development of relay protection and fault location technology based on high-frequency transient information.

[0159] Based on the above analytical calculation method of transient voltage and current of power grid fault, Fig.13 As shown, an embodiment of the present invention provides a system for analyzing and calculating transient voltage and current of a power grid fault, comprising:

[0160] A fault resistor network matrix construction module 01 is used to construct a corresponding fault resistor network matrix based on at least the fault type of the target power system;

[0161] The voltage and current initial traveling wave calculation module 02 is used to calculate the voltage and current initial traveling waves at the fault point by using phase mode transformation based on at least the fault resistance network matrix;

[0162] The fault component additional network construction module 03 is used to construct a fault component additional network based on the initial traveling wave and cross transmission of the voltage and current at the fault point; wherein the fault component additional network is in the form of a weighted directed graph and includes a zero mode network and a line mode network, the zero mode network includes a zero mode measurement point, and the line mode network includes a line mode measurement point;

[0163] The traveling wave refraction reflection coefficient calculation module 04 is used to calculate the first traveling wave refraction reflection coefficient at the fault point and the second traveling wave refraction reflection coefficient at the non-fault point in the fault component additional network based on the fault point characteristics; wherein the fault point characteristics include connecting the zero mode network and the line mode network;

[0164] The traveling wave propagation path calculation module 05 is used to respectively obtain all first traveling wave propagation paths from the fault point to the zero mode measurement point and all second traveling wave propagation paths from the fault point to the line mode measurement point, and calculate the total propagation time and the total traveling wave refraction reflection coefficient on each traveling wave propagation path based on at least the first traveling wave refraction reflection coefficient and the second traveling wave refraction reflection coefficient;

[0165] The fault transient voltage and current analysis module 06 is used to obtain the fault transient voltage and current analysis formula by summing and superposition based on at least the total propagation time and the total traveling wave refraction reflection coefficient.

[0166] It should be noted that each module in the above-mentioned system for analyzing and calculating transient voltage and current of power grid faults can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory in the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules. For the specific definition of a system for analyzing and calculating transient voltage and current of power grid faults, please refer to the definition of a method for analyzing and calculating transient voltage and current of power grid faults in the above text. The two have the same functions and effects, which will not be repeated here.

[0167] An embodiment of the present invention further provides a terminal device, the terminal device comprising:

[0168] processor, memory, and bus;

[0169] The bus is used to connect the processor and the memory;

[0170] The memory is used to store operation instructions;

[0171] The processor is used to call the operation instruction, and the executable instruction enables the processor to perform operations corresponding to the analytical calculation method for transient voltage and current of power grid fault as described above in the present invention.

[0172] In an optional embodiment, a terminal device is provided, such as Fig.14 As shown, Fig.14 The terminal device 5000 shown includes: a processor 5001 and a memory 5003. The processor 5001 and the memory 5003 are connected, such as through a bus 5002. Optionally, the terminal device 5000 may also include a transceiver 5004. It should be noted that in actual applications, the transceiver 5004 is not limited to one, and the structure of the terminal device 5000 does not constitute a limitation on the embodiments of the present invention.

[0173] Processor 5001 may be a CPU, a general-purpose processor, a DSP, an ASIC, an FPGA or other programmable logic device, a transistor logic device, a hardware component or any combination thereof. It may implement or execute various exemplary logic blocks, modules and circuits described in conjunction with the disclosure of the present invention. Processor 5001 may also be a combination that implements computing functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, etc.

[0174] The bus 5002 may include a path to transmit information between the above components. The bus 5002 may be a PCI bus or an EISA bus, etc. The bus 5002 may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Fig.14Only one thick line is used in the diagram, but this does not mean that there is only one bus or only one type of bus.

[0175] The memory 5003 may be a ROM or other type of static storage device that can store static information and instructions, a RAM or other type of dynamic storage device that can store information and instructions, or an EEPROM, a CD-ROM or other optical disk storage, an optical disk storage (including a compressed optical disk, a laser disk, an optical disk, a digital versatile disk, a Blu-ray disk, etc.), a magnetic disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited to these.

[0176] The memory 5003 is used to store application code for executing the solution of the present invention, and the execution is controlled by the processor 5001. The processor 5001 is used to execute the application code stored in the memory 5003 to implement the content shown in any of the above method embodiments.

[0177] In summary, the analytical calculation method, system and device of transient voltage and current of power grid fault in the embodiment of the present invention can obtain the analytical expression of transient voltage and current of power grid fault, which has clear mathematical and physical meanings and is suitable for various fault types, different fault transition resistances, different power grid topologies and different line parameters. For uniformly transposed lossless lines, without considering the parameter-dependent characteristics, the analytical expression obtained is completely accurate, thereby providing a reliable theoretical basis for the development of relay protection and fault location technology based on high-frequency transient information.

[0178] Each embodiment in this specification is described in a progressive manner, and the same or similar parts of each embodiment can be directly referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. It should be noted that the technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above-mentioned embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0179] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention. These improvements and substitutions should also be regarded as the scope of protection of the present invention.

Claims

1. A method for calculating transient voltage and current of a power grid fault, characterized in that: include: At least based on the fault type of the target power system, construct a corresponding fault resistor network matrix; At least based on the fault resistance network matrix, using phase mode transformation to calculate the initial traveling waves of voltage and current at the fault point; Based on the initial traveling waves and cross transmissions of the voltage and current at the fault point, construct a fault component additional network; wherein the fault component additional network is in the form of a weighted directed graph and includes a zero mode network and a line mode network, the zero mode network includes a zero mode measurement point, and the line mode network includes a line mode measurement point; Based on the fault point characteristics, respectively calculating the first row wave refraction reflection coefficient at the fault point and the second row wave refraction reflection coefficient at the non-fault point in the fault component additional network; wherein the fault point characteristics include connecting the zero mode network and the line mode network; Respectively obtain all first traveling wave propagation paths from the fault point to the zero-mode measurement point and all second traveling wave propagation paths from the fault point to the line-mode measurement point, and calculate the total propagation time and the total traveling wave refraction reflection coefficient on each traveling wave propagation path based at least on the first traveling wave refraction reflection coefficient and the second traveling wave refraction reflection coefficient; At least based on the total propagation time and the total traveling wave refraction reflection coefficient, the fault transient voltage and current analytical formula is obtained by summing and superposition.

2. The analytical calculation method according to claim 1, characterized in that: The step of constructing a corresponding fault resistance network matrix based at least on the fault type of the target power system includes: Determine a resistance network and a fault type of a target power system; wherein the resistance network includes at least a resistance connection mode; Establishing an initial equation between node voltage and node current based on electrical characteristics of the resistor network; wherein the electrical characteristics of the resistor network at least include Ohm's law; Introducing corresponding fault components into the initial equation based on the fault type to obtain a target equation; wherein the fault components include resistance changes of each resistor; The target equation is converted into a matrix form to obtain a fault resistance network matrix.

3. The analytical calculation method according to claim 1, characterized in that: The method of calculating the initial traveling waves of voltage and current at the fault point by using phase mode transformation at least based on the fault resistance network matrix comprises: Based on the corresponding relationship between the initial traveling wave phasors of voltage and current, the initial traveling wave phasor of voltage at the fault point and the initial traveling wave phasor of current flowing to one end of the bus are determined; wherein the corresponding relationship between the initial traveling wave phasors of voltage and current is characterized by the following formula: in ph +in f +2Ri ph =0 Among them, u ph represents the initial traveling wave phase of the voltage at the fault point, u f represents the voltage at the fault point before the fault occurs, R represents the fault resistance network matrix, i ph It represents the initial traveling wave phasor of the current flowing to the bus at one end; The voltage initial traveling wave modulus and the current initial traveling wave modulus are determined based on the corresponding relationship between the voltage and current initial traveling wave modulus; wherein the corresponding relationship between the voltage and current initial traveling wave modulus is characterized by the following formula: u m =Zi m Among them, u m represents the initial traveling wave modulus of voltage, i m represents the initial traveling wave modulus of the current, and Z represents the wave impedance matrix; Phase-to-mode transformation is performed based on the voltage initial traveling wave phasor, the current initial traveling wave phasor, the voltage initial traveling wave modulus and the current initial traveling wave modulus to obtain the voltage and current initial traveling waves at the fault point.

4. The analytical calculation method according to claim 3, characterized in that: The performing phase-mode transformation based on the voltage initial traveling wave phasor, the current initial traveling wave phasor, the voltage initial traveling wave modulus and the current initial traveling wave modulus to obtain the voltage and current initial traveling waves at the fault point includes: The initial voltage traveling wave phasor, the initial current traveling wave phasor, the initial voltage traveling wave modulus and the initial current traveling wave modulus are transformed into phase mode by using the Karenbauer transformation matrix to obtain the initial voltage and current traveling waves at the fault point; wherein the initial voltage and current traveling waves at the fault point are expressed by the following formula: Among them, u m represents the initial traveling wave modulus of voltage, i m represents the initial traveling wave modulus of the current, Z represents the wave impedance matrix, S represents the Karenbauer transformation matrix, R represents the fault resistance network matrix, u f Indicates the voltage at the fault point before the fault occurs.

5. The analytical calculation method according to claim 1, characterized in that: The method of constructing a fault component additional network based on the initial traveling wave and cross transmission of voltage and current at the fault point includes: Based on the initial traveling waves of voltage and current at the fault point, a zero-mode network and a line-mode network are respectively constructed; Based on the cross transmission at the fault point, the zero mode network and the fault point in the line mode network are connected to obtain an initial fault component additional network; The initial fault component additional network is characterized in the form of a weighted directed graph to obtain a fault component additional network; wherein the vertices of the weighted directed graph represent the nodes of the fault component additional network, the branches of the weighted directed graph represent the lines of the fault component additional network, the directions of the branches represent the propagation directions of the traveling waves on the lines, and the weights of the branches represent the propagation time of the traveling waves on the lines.

6. The analytical calculation method according to claim 1, characterized in that: The method of respectively calculating the first wave refraction reflection coefficient at the fault point and the second wave refraction reflection coefficient at the non-fault point in the fault component additional network based on the fault point characteristics comprises: Based on the fault point characteristics, the first line wave refraction reflection coefficient at the fault point in the fault component additional network is calculated; wherein the first line wave refraction reflection coefficient is calculated using the following formula: Among them, α represents the first wave refraction coefficient, β represents the first wave reflection coefficient, I represents the unit matrix, Z represents the wave impedance matrix, S represents the Karenbauer transformation matrix, and R represents the fault resistance network matrix; A complex frequency domain model is used to characterize the non-fault point, and the second-line wave refraction reflection coefficient at the non-fault point is calculated based on the obtained non-fault point model; wherein the non-fault point model includes a lumped parameter element connected in series between the lines and a lumped parameter element connected in parallel between the lines and the earth.

7. The analytical calculation method according to claim 1, characterized in that: The method of respectively acquiring all first traveling wave propagation paths from the fault point to the zero mode measurement point and all second traveling wave propagation paths from the fault point to the line mode measurement point, and calculating the total propagation time and the total traveling wave refraction reflection coefficient on each traveling wave propagation path based at least on the first traveling wave refraction reflection coefficient and the second traveling wave refraction reflection coefficient, comprises: Using a recursive algorithm to respectively obtain all first traveling wave propagation paths from the fault point to the zero-mode measurement point and all second traveling wave propagation paths from the fault point to the line-mode measurement point; The propagation time of all lines on each traveling wave propagation path is added up to obtain the total propagation time on the corresponding traveling wave propagation path; The traveling wave refraction and reflection coefficients of all nodes passed by each traveling wave propagation path are multiplied together to obtain the total traveling wave refraction and reflection coefficient on the corresponding traveling wave propagation path.

8. The analytical calculation method according to claim 1, characterized in that: The method of obtaining the fault transient voltage and current analytical formula by summing and superposition based at least on the total propagation time and the total traveling wave refraction reflection coefficient includes: Based on the summation operation of the total propagation time and the total traveling wave refraction and reflection coefficient, the complex frequency domain analytical expression of the traveling wave at the measurement point is obtained; wherein the complex frequency domain analytical expression of the voltage traveling wave is represented by the following formula: Among them, U mf (s) represents the voltage traveling wave complex frequency domain, γ i (s) represents the total wave refraction reflection coefficient, U i (s) represents the complex frequency domain form of the initial voltage traveling wave, s represents the complex frequency, t i represents the total propagation time; Performing an inverse Laplace transform on the complex frequency domain analytical expression of the traveling wave, and performing a phase mode transform on the obtained time domain solution to obtain a traveling wave time domain phasor; The traveling wave time domain phasors are superimposed to obtain the fault transient voltage and current analytical formula; wherein the fault transient voltage analytical formula is represented by the following formula: u m (t)=u0(t)+u mf (t) Among them, u m (t) represents the fault transient voltage, u0(t) represents the voltage at the measurement point before the fault, and u mf (t) represents the voltage traveling wave time domain phasor.

9. A system for analyzing and calculating transient voltage and current of power grid faults, characterized in that: include: A fault resistor network matrix building module, used to build a corresponding fault resistor network matrix based on at least a fault type of the target power system; A voltage and current initial traveling wave calculation module, used to calculate the voltage and current initial traveling waves at the fault point by using phase mode transformation based at least on the fault resistance network matrix; A fault component additional network construction module is used to construct a fault component additional network based on the voltage and current initial traveling waves and cross transmission at the fault point; wherein the fault component additional network is in the form of a weighted directed graph and includes a zero mode network and a line mode network, the zero mode network includes a zero mode measurement point, and the line mode network includes a line mode measurement point; A traveling wave refraction reflection coefficient calculation module is used to calculate the first traveling wave refraction reflection coefficient at the fault point and the second traveling wave refraction reflection coefficient at the non-fault point in the fault component additional network based on the fault point characteristics; wherein the fault point characteristics include connecting the zero mode network and the line mode network; A traveling wave propagation path calculation module, used to respectively obtain all first traveling wave propagation paths from the fault point to the zero-mode measurement point and all second traveling wave propagation paths from the fault point to the line-mode measurement point, and calculate the total propagation time and the total traveling wave refraction reflection coefficient on each traveling wave propagation path based at least on the first traveling wave refraction reflection coefficient and the second traveling wave refraction reflection coefficient; The fault transient voltage and current analysis module is used to obtain the fault transient voltage and current analysis formula by summing and superposition based at least on the total propagation time and the total traveling wave refraction reflection coefficient.

10. A terminal device, characterized in that: The invention comprises a processor, a memory and a computer program stored in the memory and configured to be executed by the processor, wherein when the processor executes the computer program, the analytical calculation method for transient voltage and current of a power grid fault as claimed in any one of claims 1 to 8 is implemented.

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